Oxford Cambridge and RSA
Thursday 15 May 2025 – Afternoon
AS Level Mathematics B (MEI)
H630/01 Pure Mathematics and Mechanics
Time allowed: 1 hour 30 minutes
You must have:
• the Printed Answer Booklet
• a scientific or graphical calculator
QP
INSTRUCTIONS
• Use black ink. You can use an HB pencil, but only for graphs and diagrams.
• Write your answer to each question in the space provided in the Printed Answer Booklet. If
you need extra space use the lined page at the end of the Printed Answer Booklet. The
question numbers must be clearly shown.
• Fill in the boxes on the front of the Printed Answer Booklet.
• Answer all the questions.
• Where appropriate, your answer should be supported with working. Marks might be given
for using a correct method, even if your answer is wrong.
• Give your final answers to a degree of accuracy that is appropriate to the context.
• The acceleration due to gravity is denoted by gms–2. When a numerical value is needed
use g = 9.8 unless a different value is specified in the question.
• Do not send this Question Paper for marking. Keep it in the centre or recycle it.
INFORMATION
• The total mark for this paper is 70.
• The marks for each question are shown in brackets [ ].
• This document has 8 pages.
ADVICE
• Read each question carefully before you start your answer.
OCR AS Level Mathematics B (MEI) H630/01 Pure Mathematics and Mechanics Question
paper & Marking Scheme SUMMER 2025
, 2
Formulae AS Level Mathematics B (MEI) (H630)
Binomial series
(a + b) n = an + nC1 an–1b + nC2 an–2b2 + ... + nCr an–rbr + ... +bn ^n e Nh,
C = C = JnN n!
n r n r K O=
wher r r!^n -rh!
e
LP
n^n - 1h 2 n^n - 1h...^n - r + 1h r
^1 + xhn = 1 + nx + x +... + x +... ^x 1 1, n e Rh
2! r!
Differentiation from first principles
f^x + h h -f(x)
f l(x) = lim
h"0 h
Sample variance
2 1 2 2 ^/xih2 2 2
s = n - 1Sxx where Sxx = /(xi - -x) = /xi - n = /xi -n-x
Standard deviation, s = variance
The binomial distribution
If X ~ B^n, ph then P(X = r) = nCr p r q n-r where q = 1 - p Mean
of X is np
Kinematics
Motion in a straight line
v = u + at
s = ut + 1 at2
2
s= 1 (u + v) t
2
v2 = u2 + 2as
s = vt - 12at2
© OCR 2025 H630/01 Jun25
, 3
1 Expand (2a - b) 4. You must simplify your answer. [3]
2 Triangle ABC is shown in the diagram. The length of AC is 2p cm and the length of BC is 3p cm,
where p is a positive constant. The angle ABC is 25°.
C
3p cm
2p cm
25°
A B
Calculate the size of the obtuse angle CAB. [2]
3 In this question you must show detailed reasoning.
The graph below shows the line y = 3x -4 and the line through P and Q where P is (–1, 3) and Q
is (5, 0).
y
P
Q
O 5 x
–4
Use an algebraic method to find the coordinates of the point of intersection of the two lines. [4]
© OCR 2025 H630/01 Jun25 Turn over
, 4
4 (a) Show that the equation x2 + kx - k2 = 0 has real roots for all real values of k. [2]
–1 ! 5
(b) Show that the roots of the equation x2 + kx -k2 = 0 are c mk . [2]
2
5 Two blocks A and B have masses 5 kg and 2 kg respectively. The blocks are joined together by a
light rigid horizontal bar and slide across a horizontal surface. The resistances on the blocks A and
B are modelled as 7 N and 1.75 N respectively. There are no other external horizontal forces.
(a) Calculate the acceleration of the system, according to the model. [3]
(b) In reality, the acceleration of the system is not constant. State an improvement that could
be made to the model so that it will produce results which are closer to the real situation.[1]
6 In this question you must show detailed reasoning.
Solve the equation 6 cos2x = 5 - sin x giving all the roots in the interval 0° 1 x 1 360°. [4]
–2 8
7 The point A has position vector a k. The vector AB is c m.
1 6
(a) On the axes in your Printed Answer Book, draw the position of the points A and B. [2]
(b) Calculate the distance AB. [1]
(c) Show that the midpoint of AB lies on the line y = 2x. [2]
8 On the planet Mars, acceleration due to gravity is 3.71 ms–2.
(a) Calculate the time it would take an object to fall to the planet’s surface from rest from a
point 2 m above the surface. There are no resistances to the motion of the object. [2]
(b) The mass of the object is 2.5 kg.
Calculate the magnitude of the normal contact force when the object is at rest on the
© OCR 2025 H630/01 Jun25
Thursday 15 May 2025 – Afternoon
AS Level Mathematics B (MEI)
H630/01 Pure Mathematics and Mechanics
Time allowed: 1 hour 30 minutes
You must have:
• the Printed Answer Booklet
• a scientific or graphical calculator
QP
INSTRUCTIONS
• Use black ink. You can use an HB pencil, but only for graphs and diagrams.
• Write your answer to each question in the space provided in the Printed Answer Booklet. If
you need extra space use the lined page at the end of the Printed Answer Booklet. The
question numbers must be clearly shown.
• Fill in the boxes on the front of the Printed Answer Booklet.
• Answer all the questions.
• Where appropriate, your answer should be supported with working. Marks might be given
for using a correct method, even if your answer is wrong.
• Give your final answers to a degree of accuracy that is appropriate to the context.
• The acceleration due to gravity is denoted by gms–2. When a numerical value is needed
use g = 9.8 unless a different value is specified in the question.
• Do not send this Question Paper for marking. Keep it in the centre or recycle it.
INFORMATION
• The total mark for this paper is 70.
• The marks for each question are shown in brackets [ ].
• This document has 8 pages.
ADVICE
• Read each question carefully before you start your answer.
OCR AS Level Mathematics B (MEI) H630/01 Pure Mathematics and Mechanics Question
paper & Marking Scheme SUMMER 2025
, 2
Formulae AS Level Mathematics B (MEI) (H630)
Binomial series
(a + b) n = an + nC1 an–1b + nC2 an–2b2 + ... + nCr an–rbr + ... +bn ^n e Nh,
C = C = JnN n!
n r n r K O=
wher r r!^n -rh!
e
LP
n^n - 1h 2 n^n - 1h...^n - r + 1h r
^1 + xhn = 1 + nx + x +... + x +... ^x 1 1, n e Rh
2! r!
Differentiation from first principles
f^x + h h -f(x)
f l(x) = lim
h"0 h
Sample variance
2 1 2 2 ^/xih2 2 2
s = n - 1Sxx where Sxx = /(xi - -x) = /xi - n = /xi -n-x
Standard deviation, s = variance
The binomial distribution
If X ~ B^n, ph then P(X = r) = nCr p r q n-r where q = 1 - p Mean
of X is np
Kinematics
Motion in a straight line
v = u + at
s = ut + 1 at2
2
s= 1 (u + v) t
2
v2 = u2 + 2as
s = vt - 12at2
© OCR 2025 H630/01 Jun25
, 3
1 Expand (2a - b) 4. You must simplify your answer. [3]
2 Triangle ABC is shown in the diagram. The length of AC is 2p cm and the length of BC is 3p cm,
where p is a positive constant. The angle ABC is 25°.
C
3p cm
2p cm
25°
A B
Calculate the size of the obtuse angle CAB. [2]
3 In this question you must show detailed reasoning.
The graph below shows the line y = 3x -4 and the line through P and Q where P is (–1, 3) and Q
is (5, 0).
y
P
Q
O 5 x
–4
Use an algebraic method to find the coordinates of the point of intersection of the two lines. [4]
© OCR 2025 H630/01 Jun25 Turn over
, 4
4 (a) Show that the equation x2 + kx - k2 = 0 has real roots for all real values of k. [2]
–1 ! 5
(b) Show that the roots of the equation x2 + kx -k2 = 0 are c mk . [2]
2
5 Two blocks A and B have masses 5 kg and 2 kg respectively. The blocks are joined together by a
light rigid horizontal bar and slide across a horizontal surface. The resistances on the blocks A and
B are modelled as 7 N and 1.75 N respectively. There are no other external horizontal forces.
(a) Calculate the acceleration of the system, according to the model. [3]
(b) In reality, the acceleration of the system is not constant. State an improvement that could
be made to the model so that it will produce results which are closer to the real situation.[1]
6 In this question you must show detailed reasoning.
Solve the equation 6 cos2x = 5 - sin x giving all the roots in the interval 0° 1 x 1 360°. [4]
–2 8
7 The point A has position vector a k. The vector AB is c m.
1 6
(a) On the axes in your Printed Answer Book, draw the position of the points A and B. [2]
(b) Calculate the distance AB. [1]
(c) Show that the midpoint of AB lies on the line y = 2x. [2]
8 On the planet Mars, acceleration due to gravity is 3.71 ms–2.
(a) Calculate the time it would take an object to fall to the planet’s surface from rest from a
point 2 m above the surface. There are no resistances to the motion of the object. [2]
(b) The mass of the object is 2.5 kg.
Calculate the magnitude of the normal contact force when the object is at rest on the
© OCR 2025 H630/01 Jun25
